Sample Question #263 (mathematical statistics)

You’re given *B *blue cards and *R *red cards. How many ways are there in total to shuffle these cards?

In other words, how many combinations of the blue and red cards are there?

[Source: a real interview question given at a hedge fund interview]

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ANSWER

This question is the same as asking, given B+R slots, how many ways can we arrange the B blue cards into the slots? Or equivalent, arranging the R red cards into the slots. Once cards of one color are arranged, cards of the other color can only fall into the unfilled slots.

Once you recognize this transformation of the question, you’ll see it’s a combinatorial problem. The answer is C(B+R, B) which is the same as C(B+R, R), where C() is the combination function. Finally, a "formal" solution can be written as C(B+R, min(B,R)).

Quant Career:you do NOT need the "min" in your "formal" solution. Either B or R would do just as well. Q.E.D. -Yanis